The assumption(s) in the theory of bending of beams is/are:
Try it first: pick an option, then read the explanation.
Correct answer: D. all options are correct
Asked in SSC JE 04/03/2017 (Morning)
Detailed Explanation
Simple bending theory uses several assumptions together; each listed statement is one of them.
Why “all options are correct” Is Correct
Homogeneous material, isotropic material and equal E in tension and compression are all assumed, so all options are correct.
| Assumption of simple bending | Why it is needed |
|---|---|
| Material is homogeneous and isotropic | Same E everywhere and in every direction |
| Hooke's law holds (stress within elastic limit) | Stress is proportional to strain |
| E is the same in tension and compression | Neutral axis passes through the centroid |
| Plane sections remain plane after bending | Strain varies linearly with y |
| Beam initially straight, radius of curvature large compared with depth | Simple geometry of bending |
| Beam in equilibrium under pure bending (no shear, no axial force) | Only M acts on the section |
| Each layer expands or contracts freely | Layers act independently |
Why the Other Options Are Wrong
- A. the material is homogeneous: True, but incomplete — the others are also assumptions.
- B. the material is isotropic: True, but incomplete.
- C. Young's modulus is the same in tension and in compression: True, but incomplete.
Key Point
Simple bending assumes homogeneous, isotropic, linear-elastic material with equal E in tension and compression.
Key Concepts for Students
- Equal E keeps the N.A. at the centroid.
- Plane sections remain plane gives linear strain.
- RCC and timber violate some assumptions, so design codes modify the theory.
Practice more: this is question 34 in Bending and Shear Stress MCQs – Part 3. Try the whole set and check every answer instantly.